The following line passes through point $(5, 2)$ : $y = -\dfrac{2}{3} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(5, 2)$ into the equation gives: $2 = -\dfrac{2}{3} \cdot 5 + b$ $2 = -\dfrac{10}{3} + b$ $b = 2 + \dfrac{10}{3}$ $b = \dfrac{16}{3}$ Plugging in $\dfrac{16}{3}$ for $b$, we get $y = -\dfrac{2}{3} x + \dfrac{16}{3}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(5, 2)$